Conformal restriction and Onsager-Machlup functional for SLE loop measure (Yilin Wang, IHÉS)

11.12.2023 16:15 – 18:15

Abstract:
Onsager-Machlup functional measures how likely a stochastic process stays close to a given path. SLE is a family of measures on simple paths in the plane introduced by O.Schramm obtained from the Loewner transform of a multiple of Brownian motion. We show that the Onsager-Machlup of the SLE_k loop measure, for any 0 < k \le 4, is expressed using the Loewner energy and the central charge c(k) of SLE_k. The proof relies on the conformal restriction covariance of SLE and an observation relating two ways to renormalize the Brownian loop measure. This is based on the joint work (arXiv: 2311.00209) with Marco Carfagnini (UCSD). If time permits, I will show one application of this result, which gives a representation of the Virasoro algebra using SLE loop measure. (This is work in progress with Masha Gordina and Wei Qian).

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre